Kate's shrewish behavior has isolated her from her family and she has zero marriage prospects. Petruchio comes to town looking for a rich bride and agrees to marry Kate despite her shrewishness.
Kate and Petruchio are engaged and quickly married. Petruchio sets out to tame Katherine of her shrewish ways. During their honeymoon, he behaves like a "shrew," ranting, raving, and physically abusing the servants. He also starves Kate, deprives her of sleep, and messes with her head when she refuses to obey him.
Finally, Kate breaks on the road to Bianca's wedding. She agrees to play along when Petruchio pretends the sun is the moon and an old man is a young virgin. At Bianca's wedding, Kate delivers an impassioned speech about women's duties to their husbands. The couple runs off to bed and they live happily ever after…maybe.